Join TSR now and get all your revision questions answeredSign up now

FP3 cross product proof of the direction Watch

    • Thread Starter
    Offline

    3
    ReputationRep:
    I've seen a proof of 2 vectors a,b laxbl = lallblsin(angle between them)

    https://math.la.asu.edu/~surgent/mat..._mag_proof.pdf

    but I can't find a proof on google of why the direction of the vector from the cross product of a and b is perpendicular to both of them?

    anyone got any good sites or videos, or can actually post their own proof? thanks
    Offline

    10
    ReputationRep:
    (Original post by physics4ever)
    I've seen a proof of 2 vectors a,b laxbl = lallblsin(angle between them)

    https://math.la.asu.edu/~surgent/mat..._mag_proof.pdf

    but I can't find a proof on google of why the direction of the vector from the cross product of a and b is perpendicular to both of them?

    anyone got any good sites or videos, or can actually post their own proof? thanks
    There's no proof. It's simply the part of the definition of the cross product. It's defined that way essentially because there are physical vector quantities that combine in such as way as to produce a vector that is most usefully shown as perpendicular to the plane of the other two e.g.

    a) the Lorentz force F on a moving charged particle in a magnetic field B is perpendicular to the plane containing B and the velocity vector v of the particle.

    b) if we draw a torque vector as perpendicular to the plane containing the force and displacement vectors, then we find that the torque vectors add together correctly when we have multiple forces turning an object.

    So it's defined to point in a perpendicular direction since that happens to model some physical situations nicely.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by atsruser)
    There's no proof. It's simply the part of the definition of the cross product. It's defined that way essentially because there are physical vector quantities that combine in such as way as to produce a vector that is most usefully shown as perpendicular to the plane of the other two e.g.

    a) the Lorentz force F on a moving charged particle in a magnetic field B is perpendicular to the plane containing B and the velocity vector v of the particle.

    b) if we draw a torque vector as perpendicular to the plane containing the force and displacement vectors, then we find that the torque vectors add together correctly when we have multiple forces turning an object.

    So it's defined to point in a perpendicular direction since that happens to model some physical situations nicely.
    oh yeah haha thanks! lol, they should have just put that in my textbook... rather than just giving me an equation with no explanation
 
 
 
Poll
Which Fantasy Franchise is the best?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.